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2 years ago

I

Mathematics

2 answers:

shtirl [24]2 years ago

8 0

a) 10 - 20 +45

Step-by-step explanation:

Is known :

She started with 10 points.

In the first round she lost 20 points.

In the second round she won 45 points.

Asked :

Which of the following shows the changes in Anayah scores?

Aswered :

She started with 10 points - In the first round she lost 20 points + In the second round she won 45 points

= 10 - 20 + 45

Elina [12.6K]2 years ago

5 0

Answer:

Step-by-step explanation:

It's set up exactly as it is said. She starts with 10 points automatically so you would put:

Then it says that she lost 20 points. Losing is subtraction. You would add this to the equation:

10-20

Then it says she won 45 points. Winning is addition. You would add this to the equation:

10-20+45

This equation matches up with A. thus A. being the correct answer. If they ask for the answer, it is 35 by the way. Hope this helps!

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3 years ago

Please help solve for x..

aalyn [17]

Answer:

x = 1 or x = -1

Step-by-step explanation:

Given equation:

$x^{100}-4^x \cdot x^{98}-x^2+4^x=0$

Factor out -1:

$\implies -1(-x^{100}+4^x \cdot x^{98}+x^2-4^x)=0$

Divide both sides by -1:

$\implies -x^{100}+4^x \cdot x^{98}+x^2-4^x=0$

Rearrange the terms:

$\implies 4^x \cdot x^{98}-4^x-x^{100}+x^2=0$

$\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c \quad \textsf{to }x^{100}:$

$\implies 4^x \cdot x^{98}-4^x-x^{98}x^2+x^2=0$

Factor the first two terms and the last two terms separately:

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Factor out the common term $(x^{98}-1)$ :

$\implies (4^x-x^2)(x^{98}-1)=0$

<u>Zero Product Property</u>: If a ⋅ b = 0 then either a = 0 or b = 0 (or both).

Using the <u>Zero Product Property</u>, set each factor equal to zero and solve for x (if possible):

$\begin{aligned}x^{98}-1 & = 0 & \quad \textsf{or} \quad \quad4^x-x^2 & = 0 \\x^{98} & =1 & 4^x & = x^2 \\x & = 1, -1 & \textsf{no}& \textsf{ solutions for } x \in \mathbb{R}\end{aligned}$

Therefore, the solutions to the given equation are: x = 1 or x = -1

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1 year ago